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<div class="sect1">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="array_types"></a>Array Components</h2></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="sect2"><a href="array_types.html#multi_array_class"><code class="literal">multi_array</code></a></span></dt>
<dt><span class="sect2"><a href="array_types.html#multi_array_ref"><code class="literal">multi_array_ref</code></a></span></dt>
<dt><span class="sect2"><a href="array_types.html#const_multi_array_ref"><code class="literal">const_multi_array_ref</code></a></span></dt>
</dl></div>
<p>
Boost.MultiArray defines an array class,
<code class="literal">multi_array</code>, and two adapter classes,
<code class="literal">multi_array_ref</code> and 
<code class="literal">const_multi_array_ref</code>. The three classes model 
MultiArray and so they share a lot of functionality.
<code class="literal">multi_array_ref</code> differs from
<code class="literal">multi_array</code> in that the
<code class="literal">multi_array</code> manages its own memory, while
<code class="literal">multi_array_ref</code> is passed a block of memory that it
expects to be externally managed.
<code class="literal">const_multi_array_ref</code> differs from
<code class="literal">multi_array_ref</code> in that the underlying elements it
adapts cannot be modified through its interface, though some array
properties, including the array shape and index bases, can be altered.
Functionality the classes have in common is described
below.
</p>
<p><b>Note: Preconditions, Effects, and Implementation. </b>
Throughout the following sections, small pieces of C++ code are
used to specify constraints such as preconditions, effects, and
postconditions.  These do not necessarily describe the underlying
implementation of array components; rather, they describe the 
expected input to and
behavior of the specified operations.  Failure to meet
preconditions results in undefined behavior. Not all effects
(i.e. copy constructors, etc.) must be mimicked exactly.  The code
snippets for effects intend to capture the essence of the described
operation. 
</p>
<p><b>Queries. </b></p>
<div class="variablelist"><dl class="variablelist">
<dt><span class="term"><pre class="programlisting">element* data();
const element* data() const;</pre></span></dt>
<dd><p>This returns a pointer to the beginning of the
contiguous block that contains the array's data. If all dimensions of
the array are 0-indexed and stored in ascending order, this is 
equivalent to <code class="literal">origin()</code>. Note that
<code class="literal">const_multi_array_ref</code> only provides the const
version of this function.
</p></dd>
<dt><span class="term"><pre class="programlisting">element* origin();
const element* origin() const;</pre></span></dt>
<dd><p>This returns the origin element of the
<code class="literal">multi_array</code>. Note that
<code class="literal">const_multi_array_ref</code> only provides the const
version of this function. (Required by MultiArray)
</p></dd>
<dt><span class="term"><code class="function">const index* index_bases();</code></span></dt>
<dd><p>This returns the index bases for the
<code class="literal">multi_array</code>. (Required by MultiArray)
</p></dd>
<dt><span class="term"><code class="function">const index* strides();</code></span></dt>
<dd><p>This returns the strides for the
<code class="literal">multi_array</code>. (Required by MultiArray)
</p></dd>
<dt><span class="term"><code class="function">const size_type* shape();</code></span></dt>
<dd><p>This returns the shape of the
<code class="literal">multi_array</code>. (Required by MultiArray)
</p></dd>
</dl></div>
<p><b>Comparators. </b></p>
<div class="variablelist"><dl class="variablelist">
<dt><span class="term"><pre class="programlisting">
bool operator==(const *array-type*&amp; rhs);
bool operator!=(const *array-type*&amp; rhs);
bool operator&lt;(const *array-type*&amp; rhs);
bool operator&gt;(const *array-type*&amp; rhs);
bool operator&gt;=(const *array-type*&amp; rhs);
bool operator&lt;=(const *array-type*&amp; rhs);</pre></span></dt>
<dd>
<p>Each comparator executes a lexicographical compare over
the value types of the two arrays.
(Required by MultiArray)
</p>
<p><b>Preconditions. </b><code class="literal">element</code> must support the
comparator corresponding to that called on
<code class="literal">multi_array</code>.</p>
<p><b>Complexity. </b>O(<code class="literal">num_elements()</code>).</p>
</dd>
</dl></div>
<p><b>Modifiers. </b></p>
<div class="variablelist"><dl class="variablelist">
<dt><span class="term">
<pre class="programlisting">

template &lt;typename SizeList&gt;
void reshape(const SizeList&amp; sizes)

</pre>
</span></dt>
<dd>
<p>This changes the shape of the <code class="literal">multi_array</code>.  The
number of elements and the index bases remain the same, but the number
of values at each level of the nested container hierarchy may
change.</p>
<p><b><code class="literal">SizeList</code> Requirements. </b><code class="literal">SizeList</code> must model
<a href="../../utility/Collection.html" target="_top">Collection</a>.</p>
<p><b>Preconditions. </b>
</p>
<pre class="programlisting">
std::accumulate(sizes.begin(),sizes.end(),size_type(1),std::times&lt;size_type&gt;()) == this-&gt;num_elements();
sizes.size() == NumDims;
</pre>
<p><b>Postconditions. </b>
<code class="literal">std::equal(sizes.begin(),sizes.end(),this-&gt;shape) == true;</code>
</p>
</dd>
<dt><span class="term">
<pre class="programlisting">

template &lt;typename BaseList&gt;
void reindex(const BaseList&amp; values);

</pre>
</span></dt>
<dd>
<p>This changes the index bases of the <code class="literal">multi_array</code> to
correspond to the the values in <code class="literal">values</code>.</p>
<p><b><code class="literal">BaseList</code> Requirements. </b><code class="literal">BaseList</code> must model
<a href="../../utility/Collection.html" target="_top">Collection</a>.</p>
<p><b>Preconditions. </b><code class="literal">values.size() == NumDims;</code></p>
<p><b>Postconditions. </b><code class="literal">std::equal(values.begin(),values.end(),this-&gt;index_bases());
</code></p>
</dd>
<dt><span class="term">
<pre class="programlisting">

void reindex(index value);

</pre>
</span></dt>
<dd>
<p>This changes the index bases of all dimensions of the
<code class="literal">multi_array</code> to <code class="literal">value</code>.</p>
<p><b>Postconditions. </b>
</p>
<pre class="programlisting">

std::count_if(this-&gt;index_bases(),this-&gt;index_bases()+this-&gt;num_dimensions(),
              std::bind_2nd(std::equal_to&lt;index&gt;(),value)) == 
              this-&gt;num_dimensions();

</pre>
<p>
</p>
</dd>
</dl></div>
<div class="sect2">
<div class="titlepage"><div><div><h3 class="title">
<a name="multi_array_class"></a><code class="literal">multi_array</code>
</h3></div></div></div>
<p>
<code class="literal">multi_array</code> is a multi-dimensional container that
supports random access iteration. Its number of dimensions is
fixed at compile time, but its shape and the number of elements it
contains are specified during its construction. The number of elements
will remain fixed for the duration of a
<code class="literal">multi_array</code>'s lifetime, but the shape of the container can
be changed. A <code class="literal">multi_array</code> manages its data elements
using a replaceable allocator.
</p>
<p><b>Model Of. </b>
<a class="link" href="MultiArray.html" title="MultiArray Concept">MultiArray</a>,
<a href="../../../libs/utility/CopyConstructible.html" target="_top">CopyConstructible</a>. Depending on the element type, 
it may also model <a href="https://www.boost.org/sgi/stl/EqualityComparable.html" target="_top">EqualityComparable</a> and <a href="https://www.boost.org/sgi/stl/LessThanComparable.html" target="_top">LessThanComparable</a>. 
</p>
<p><b>Synopsis. </b></p>
<pre class="programlisting">

namespace boost {

template &lt;typename ValueType, 
          std::size_t NumDims, 
          typename Allocator = std::allocator&lt;ValueType&gt; &gt;
class multi_array {
public:
// types:
  typedef ValueType                             element;
  typedef *unspecified*                         value_type;
  typedef *unspecified*                         reference;
  typedef *unspecified*                         const_reference;
  typedef *unspecified*                         difference_type;
  typedef *unspecified*                         iterator;
  typedef *unspecified*                         const_iterator;
  typedef *unspecified*                         reverse_iterator;
  typedef *unspecified*                         const_reverse_iterator;
  typedef multi_array_types::size_type          size_type;
  typedef multi_array_types::index              index;
  typedef multi_array_types::index_gen          index_gen;
  typedef multi_array_types::index_range        index_range;
  typedef multi_array_types::extent_gen         extent_gen;
  typedef multi_array_types::extent_range       extent_range;
  typedef *unspecified*                         storage_order_type;


  // template typedefs
  template &lt;std::size_t Dims&gt; struct            subarray;
  template &lt;std::size_t Dims&gt; struct            const_subarray;
  template &lt;std::size_t Dims&gt; struct            array_view;
  template &lt;std::size_t Dims&gt; struct            const_array_view;
  

  static const std::size_t dimensionality = NumDims;
  

  // constructors and destructors

  multi_array(const Allocator&amp; alloc = Allocator());

  template &lt;typename ExtentList&gt;
  explicit multi_array(const ExtentList&amp; sizes,
                       const storage_order_type&amp; store = c_storage_order(),
                       const Allocator&amp; alloc = Allocator());
  explicit multi_array(const extents_tuple&amp; ranges,
                       const storage_order_type&amp; store = c_storage_order(),
	               const Allocator&amp; alloc = Allocator());
  multi_array(const multi_array&amp; x);
  multi_array(const const_multi_array_ref&lt;ValueType,NumDims&gt;&amp; x,
              const Allocator&amp; alloc = Allocator());
  multi_array(const const_subarray&lt;NumDims&gt;::type&amp; x,
              const Allocator&amp; alloc = Allocator());
  multi_array(const const_array_view&lt;NumDims&gt;::type&amp; x,
              const Allocator&amp; alloc = Allocator());

  multi_array(const multi_array_ref&lt;ValueType,NumDims&gt;&amp; x,
              const Allocator&amp; alloc = Allocator());
  multi_array(const subarray&lt;NumDims&gt;::type&amp; x,
              const Allocator&amp; alloc = Allocator());
  multi_array(const array_view&lt;NumDims&gt;::type&amp; x,
              const Allocator&amp; alloc = Allocator());

  ~multi_array();

  // modifiers

  multi_array&amp; operator=(const multi_array&amp; x);
  template &lt;class Array&gt; multi_array&amp; operator=(const Array&amp; x);

  // iterators:
  iterator				begin();
  iterator				end();
  const_iterator			begin() const;
  const_iterator			end() const;
  reverse_iterator			rbegin();
  reverse_iterator			rend();
  const_reverse_iterator		rbegin() const;
  const_reverse_iterator		rend() const;

  // capacity:
  size_type				size() const;
  size_type				num_elements() const;
  size_type				num_dimensions() const;
 
  // element access:
  template &lt;typename IndexList&gt; 
    element&amp;			operator()(const IndexList&amp; indices);
  template &lt;typename IndexList&gt;
    const element&amp;		operator()(const IndexList&amp; indices) const;
  reference			operator[](index i);
  const_reference		operator[](index i) const;
  array_view&lt;Dims&gt;::type	operator[](const indices_tuple&amp; r);
  const_array_view&lt;Dims&gt;::type	operator[](const indices_tuple&amp; r) const;

  // queries
  element*			data();
  const element*		data() const;
  element*			origin();
  const element*		origin() const;
  const size_type*		shape() const;
  const index*			strides() const;
  const index*			index_bases() const;
  const storage_order_type&amp;     storage_order() const;

  // comparators
  bool operator==(const multi_array&amp; rhs);
  bool operator!=(const multi_array&amp; rhs);
  bool operator&lt;(const multi_array&amp; rhs);
  bool operator&gt;(const multi_array&amp; rhs);
  bool operator&gt;=(const multi_array&amp; rhs);
  bool operator&lt;=(const multi_array&amp; rhs);

  // modifiers:
  template &lt;typename InputIterator&gt;
    void			assign(InputIterator begin, InputIterator end);
  template &lt;typename SizeList&gt;
    void			reshape(const SizeList&amp; sizes)
  template &lt;typename BaseList&gt;	void reindex(const BaseList&amp; values);
    void			reindex(index value);
  template &lt;typename ExtentList&gt;
    multi_array&amp;		resize(const ExtentList&amp; extents);
  multi_array&amp;                  resize(extents_tuple&amp; extents);
};

</pre>
<p><b>Constructors. </b></p>
<div class="variablelist"><dl class="variablelist">
<dt><span class="term"><pre class="programlisting">template &lt;typename ExtentList&gt;
explicit multi_array(const ExtentList&amp; sizes,
                     const storage_order_type&amp; store = c_storage_order(),
                     const Allocator&amp; alloc = Allocator());
</pre></span></dt>
<dd>
<p>
This constructs a <code class="literal">multi_array</code> using the specified
parameters.  <code class="literal">sizes</code> specifies the shape of the
constructed <code class="literal">multi_array</code>.  <code class="literal">store</code>
specifies the storage order or layout in memory of the array
dimensions.  <code class="literal">alloc</code> is used to
allocate the contained elements.
</p>
<p><b><code class="literal">ExtentList</code> Requirements. </b>
<code class="literal">ExtentList</code> must model <a href="../../utility/Collection.html" target="_top">Collection</a>.
</p>
<p><b>Preconditions. </b><code class="literal">sizes.size() == NumDims;</code></p>
</dd>
<dt><span class="term">
<pre class="programlisting">explicit multi_array(extent_gen::gen_type&lt;NumDims&gt;::type ranges,
                     const storage_order_type&amp; store = c_storage_order(),
                     const Allocator&amp; alloc = Allocator());
</pre></span></dt>
<dd><p>
This constructs a <code class="literal">multi_array</code> using the specified
    parameters.  <code class="literal">ranges</code> specifies the shape and
index bases of the constructed multi_array. It is the result of 
<code class="literal">NumDims</code> chained calls to 
    <code class="literal">extent_gen::operator[]</code>. <code class="literal">store</code>
specifies the storage order or layout in memory of the array
dimensions.  <code class="literal">alloc</code> is the allocator used to
allocate the memory used to store <code class="literal">multi_array</code>
elements.
</p></dd>
<dt><span class="term"><pre class="programlisting">
multi_array(const multi_array&amp; x);
multi_array(const const_multi_array_ref&lt;ValueType,NumDims&gt;&amp; x,
    const Allocator&amp; alloc = Allocator());
multi_array(const const_subarray&lt;NumDims&gt;::type&amp; x,
    const Allocator&amp; alloc = Allocator());
multi_array(const const_array_view&lt;NumDims&gt;::type&amp; x,
    const Allocator&amp; alloc = Allocator());
multi_array(const multi_array_ref&lt;ValueType,NumDims&gt;&amp; x,
    const Allocator&amp; alloc = Allocator());
multi_array(const subarray&lt;NumDims&gt;::type&amp; x,
    const Allocator&amp; alloc = Allocator());
multi_array(const array_view&lt;NumDims&gt;::type&amp; x,
    const Allocator&amp; alloc = Allocator());
</pre></span></dt>
<dd>
<p>These constructors all constructs a <code class="literal">multi_array</code> and 
perform a deep copy of <code class="literal">x</code>. 
</p>
<p><b>Complexity. </b> This performs O(<code class="literal">x.num_elements()</code>) calls to
<code class="literal">element</code>'s copy 
constructor.
</p>
</dd>
<dt><span class="term"><pre class="programlisting">
multi_array();
</pre></span></dt>
<dd><p>This constructs a <code class="literal">multi_array</code> whose shape is (0,...,0) and contains no elements.
</p></dd>
</dl></div>
<p><b>Note on Constructors. </b>
The  <code class="literal">multi_array</code> construction expressions,
</p>
<pre class="programlisting">
     multi_array&lt;int,3&gt; A(boost::extents[5][4][3]);
</pre>
<p>
and
</p>
<pre class="programlisting">
     boost::array&lt;multi_array_base::index,3&gt; my_extents = {{5, 4, 3}};
     multi_array&lt;int,3&gt; A(my_extents);
</pre>
<p>
are equivalent.
</p>
<p><b>Modifiers. </b></p>
<div class="variablelist"><dl class="variablelist">
<dt><span class="term"><pre class="programlisting">
multi_array&amp; operator=(const multi_array&amp; x);
template &lt;class Array&gt; multi_array&amp; operator=(const Array&amp; x);
</pre>
</span></dt>
<dd>
<p>This performs an element-wise copy of <code class="literal">x</code>
into the current <code class="literal">multi_array</code>.</p>
<p><b><code class="literal">Array</code> Requirements. </b><code class="literal">Array</code> must model MultiArray. 
</p>
<p><b>Preconditions. </b>
</p>
<pre class="programlisting">std::equal(this-&gt;shape(),this-&gt;shape()+this-&gt;num_dimensions(),
x.shape());</pre>
<p><b>Postconditions. </b>
</p>
<pre class="programlisting">(*.this) == x;</pre>
<p>
</p>
<p><b>Complexity. </b>The assignment operators perform 
O(<code class="literal">x.num_elements()</code>) calls to <code class="literal">element</code>'s 
copy constructor.</p>
</dd>
<dt><span class="term">
<pre class="programlisting">

template &lt;typename InputIterator&gt;
void assign(InputIterator begin, InputIterator end);
</pre>
</span></dt>
<dd>
<p>This copies the elements in the range 
<code class="literal">[begin,end)</code> into the array.  It is equivalent to 
<code class="literal">std::copy(begin,end,this-&gt;data())</code>.
</p>
<p><b>Preconditions. </b><code class="literal">std::distance(begin,end) == this-&gt;num_elements();</code>
</p>
<p><b>Complexity. </b>
The <code class="literal">assign</code> member function performs
O(<code class="literal">this-&gt;num_elements()</code>) calls to
<code class="literal">ValueType</code>'s copy constructor.
</p>
</dd>
<dt><span class="term">
<pre class="programlisting">multi_array&amp; resize(extent_gen::gen_type&lt;NumDims&gt;::type extents);
template &lt;typename ExtentList&gt;
  multi_array&amp; resize(const ExtentList&amp; extents);

</pre></span></dt>
<dd><p>
This function resizes an array to the shape specified by
<code class="literal">extents</code>, which is either a generated list of
extents or a model of the <code class="literal">Collection</code> concept. The
contents of the array are preserved whenever possible; if the new
array size is smaller, then some data will be lost. Any new elements
created by resizing the array are initialized with the
<code class="literal">element</code> default constructor.
</p></dd>
</dl></div>
<p><b>Queries. </b></p>
<div class="variablelist"><dl class="variablelist">
<dt><span class="term"><pre class="programlisting">
storage_order_type&amp; storage_order() const;
</pre>
</span></dt>
<dd><p>This query returns the storage order object associated with the 
<code class="literal">multi_array</code> in question.  It can be used to construct a new array with the same storage order.</p></dd>
</dl></div>
</div>
<div class="sect2">
<div class="titlepage"><div><div><h3 class="title">
<a name="multi_array_ref"></a><code class="literal">multi_array_ref</code>
</h3></div></div></div>
<p>
<code class="literal">multi_array_ref</code> is a multi-dimensional container
adaptor.  It provides the MultiArray interface over any contiguous
block of elements.  <code class="literal">multi_array_ref</code> exports the
same interface as <code class="literal">multi_array</code>, with the exception
of the constructors.
</p>
<p><b>Model Of. </b>
<code class="literal">multi_array_ref</code> models 
<a class="link" href="MultiArray.html" title="MultiArray Concept">MultiArray</a>,
<a href="../../../libs/utility/CopyConstructible.html" target="_top">CopyConstructible</a>.
and depending on the element type, it may also model
<a href="https://www.boost.org/sgi/stl/EqualityComparable.html" target="_top">EqualityComparable</a> and <a href="https://www.boost.org/sgi/stl/LessThanComparable.html" target="_top">LessThanComparable</a>. 
Detailed descriptions are provided here only for operations that are
not described in the <code class="literal">multi_array</code> reference.
</p>
<p><b>Synopsis. </b></p>
<pre class="programlisting">

namespace boost {

template &lt;typename ValueType, 
          std::size_t NumDims&gt;
class multi_array_ref {
public:
// types:
  typedef ValueType                             element;
  typedef *unspecified*                         value_type;
  typedef *unspecified*                         reference;
  typedef *unspecified*                         const_reference;
  typedef *unspecified*                         difference_type;
  typedef *unspecified*                         iterator;
  typedef *unspecified*                         const_iterator;
  typedef *unspecified*                         reverse_iterator;
  typedef *unspecified*                         const_reverse_iterator;
  typedef multi_array_types::size_type          size_type;
  typedef multi_array_types::index              index;
  typedef multi_array_types::index_gen          index_gen;
  typedef multi_array_types::index_range        index_range;
  typedef multi_array_types::extent_gen         extent_gen;
  typedef multi_array_types::extent_range       extent_range;
  typedef *unspecified*                         storage_order_type;
  
  // template typedefs
  template &lt;std::size_t Dims&gt; struct            subarray;
  template &lt;std::size_t Dims&gt; struct            const_subarray;
  template &lt;std::size_t Dims&gt; struct            array_view;
  template &lt;std::size_t Dims&gt; struct            const_array_view;
  

  static const std::size_t dimensionality = NumDims;


  // constructors and destructors

  template &lt;typename ExtentList&gt;
  explicit multi_array_ref(element* data, const ExtentList&amp; sizes,
                       const storage_order_type&amp; store = c_storage_order());
  explicit multi_array_ref(element* data, const extents_tuple&amp; ranges,
                       const storage_order_type&amp; store = c_storage_order());
  multi_array_ref(const multi_array_ref&amp; x);
  ~multi_array_ref();

  // modifiers

  multi_array_ref&amp; operator=(const multi_array_ref&amp; x);
  template &lt;class Array&gt; multi_array_ref&amp; operator=(const Array&amp; x);

  // iterators:
  iterator				begin();
  iterator				end();
  const_iterator			begin() const;
  const_iterator			end() const;
  reverse_iterator			rbegin();
  reverse_iterator			rend();
  const_reverse_iterator		rbegin() const;
  const_reverse_iterator		rend() const;

  // capacity:
  size_type				size() const;
  size_type				num_elements() const;
  size_type				num_dimensions() const;
 
  // element access:
  template &lt;typename IndexList&gt; 
    element&amp;			operator()(const IndexList&amp; indices);
  template &lt;typename IndexList&gt;
    const element&amp;		operator()(const IndexList&amp; indices) const;
  reference			operator[](index i);
  const_reference		operator[](index i) const;
  array_view&lt;Dims&gt;::type	operator[](const indices_tuple&amp; r);
  const_array_view&lt;Dims&gt;::type	operator[](const indices_tuple&amp; r) const;

  // queries
  element*			data();
  const element*		data() const;
  element*			origin();
  const element*		origin() const;
  const size_type*		shape() const;
  const index*			strides() const;
  const index*			index_bases() const;
  const storage_order_type&amp;     storage_order() const;

  // comparators
  bool operator==(const multi_array_ref&amp; rhs);
  bool operator!=(const multi_array_ref&amp; rhs);
  bool operator&lt;(const multi_array_ref&amp; rhs);
  bool operator&gt;(const multi_array_ref&amp; rhs);
  bool operator&gt;=(const multi_array_ref&amp; rhs);
  bool operator&lt;=(const multi_array_ref&amp; rhs);

  // modifiers:
  template &lt;typename InputIterator&gt;
    void			assign(InputIterator begin, InputIterator end);
  template &lt;typename SizeList&gt;
    void			reshape(const SizeList&amp; sizes)
  template &lt;typename BaseList&gt;	void reindex(const BaseList&amp; values);
  void				reindex(index value);
};

</pre>
<p><b>Constructors. </b></p>
<div class="variablelist"><dl class="variablelist">
<dt><span class="term"><pre class="programlisting">template &lt;typename ExtentList&gt;
explicit multi_array_ref(element* data, 
                     const ExtentList&amp; sizes,
                     const storage_order&amp; store = c_storage_order(),
                     const Allocator&amp; alloc = Allocator());
</pre></span></dt>
<dd>
<p>
This constructs a <code class="literal">multi_array_ref</code> using the specified
parameters.  <code class="literal">sizes</code> specifies the shape of the
constructed <code class="literal">multi_array_ref</code>.  <code class="literal">store</code>
specifies the storage order or layout in memory of the array
dimensions.  <code class="literal">alloc</code> is used to
allocate the contained elements.
</p>
<p><b><code class="literal">ExtentList</code> Requirements. </b>
<code class="literal">ExtentList</code> must model <a href="../../utility/Collection.html" target="_top">Collection</a>.
</p>
<p><b>Preconditions. </b><code class="literal">sizes.size() == NumDims;</code></p>
</dd>
<dt><span class="term">
<pre class="programlisting">explicit multi_array_ref(element* data,
                     extent_gen::gen_type&lt;NumDims&gt;::type ranges,
                     const storage_order&amp; store = c_storage_order());
</pre></span></dt>
<dd><p>
This constructs a <code class="literal">multi_array_ref</code> using the specified
    parameters.  <code class="literal">ranges</code> specifies the shape and
index bases of the constructed multi_array_ref. It is the result of 
<code class="literal">NumDims</code> chained calls to 
    <code class="literal">extent_gen::operator[]</code>. <code class="literal">store</code>
specifies the storage order or layout in memory of the array
dimensions. 
</p></dd>
<dt><span class="term"><pre class="programlisting">
multi_array_ref(const multi_array_ref&amp; x);
</pre></span></dt>
<dd>
<p>This constructs a shallow copy of <code class="literal">x</code>.
</p>
<p><b>Complexity. </b> Constant time (for contrast, compare this to
the <code class="literal">multi_array</code> class copy constructor.
</p>
</dd>
</dl></div>
<p><b>Modifiers. </b></p>
<div class="variablelist"><dl class="variablelist">
<dt><span class="term"><pre class="programlisting">
multi_array_ref&amp; operator=(const multi_array_ref&amp; x);
template &lt;class Array&gt; multi_array_ref&amp; operator=(const Array&amp; x);
</pre>
</span></dt>
<dd>
<p>This performs an element-wise copy of <code class="literal">x</code>
into the current <code class="literal">multi_array_ref</code>.</p>
<p><b><code class="literal">Array</code> Requirements. </b><code class="literal">Array</code> must model MultiArray. 
</p>
<p><b>Preconditions. </b>
</p>
<pre class="programlisting">std::equal(this-&gt;shape(),this-&gt;shape()+this-&gt;num_dimensions(),
x.shape());</pre>
<p><b>Postconditions. </b>
</p>
<pre class="programlisting">(*.this) == x;</pre>
<p>
</p>
<p><b>Complexity. </b>The assignment operators perform 
O(<code class="literal">x.num_elements()</code>) calls to <code class="literal">element</code>'s 
copy constructor.</p>
</dd>
</dl></div>
</div>
<div class="sect2">
<div class="titlepage"><div><div><h3 class="title">
<a name="const_multi_array_ref"></a><code class="literal">const_multi_array_ref</code>
</h3></div></div></div>
<p>
<code class="literal">const_multi_array_ref</code> is a multi-dimensional container
adaptor.  It provides the MultiArray interface over any contiguous
block of elements.  <code class="literal">const_multi_array_ref</code> exports the
same interface as <code class="literal">multi_array</code>, with the exception
of the constructors.
</p>
<p><b>Model Of. </b>
<code class="literal">const_multi_array_ref</code> models
<a class="link" href="MultiArray.html" title="MultiArray Concept">MultiArray</a>,
<a href="../../../libs/utility/CopyConstructible.html" target="_top">CopyConstructible</a>.
and depending on the element type, it may also model
<a href="https://www.boost.org/sgi/stl/EqualityComparable.html" target="_top">EqualityComparable</a> and <a href="https://www.boost.org/sgi/stl/LessThanComparable.html" target="_top">LessThanComparable</a>. 

Detailed descriptions are provided here only for operations that are
not described in the <code class="literal">multi_array</code> reference.
</p>
<p><b>Synopsis. </b></p>
<pre class="programlisting">

namespace boost {

template &lt;typename ValueType, 
          std::size_t NumDims, 
          typename TPtr = const T*&gt;
class const_multi_array_ref {
public:
// types:
  typedef ValueType                             element;
  typedef *unspecified*                         value_type;
  typedef *unspecified*                         reference;
  typedef *unspecified*                         const_reference;
  typedef *unspecified*                         difference_type;
  typedef *unspecified*                         iterator;
  typedef *unspecified*                         const_iterator;
  typedef *unspecified*                         reverse_iterator;
  typedef *unspecified*                         const_reverse_iterator;
  typedef multi_array_types::size_type          size_type;
  typedef multi_array_types::index              index;
  typedef multi_array_types::index_gen          index_gen;
  typedef multi_array_types::index_range        index_range;
  typedef multi_array_types::extent_gen         extent_gen;
  typedef multi_array_types::extent_range       extent_range;
  typedef *unspecified*                         storage_order_type;
  
  // template typedefs
  template &lt;std::size_t Dims&gt; struct            subarray;
  template &lt;std::size_t Dims&gt; struct            const_subarray;
  template &lt;std::size_t Dims&gt; struct            array_view;
  template &lt;std::size_t Dims&gt; struct            const_array_view;
  

  // structors

  template &lt;typename ExtentList&gt;
  explicit const_multi_array_ref(TPtr data, const ExtentList&amp; sizes,
                       const storage_order_type&amp; store = c_storage_order());
  explicit const_multi_array_ref(TPtr data, const extents_tuple&amp; ranges,
                       const storage_order_type&amp; store = c_storage_order());
  const_multi_array_ref(const const_multi_array_ref&amp; x);
  ~const_multi_array_ref();



  // iterators:
  const_iterator			begin() const;
  const_iterator			end() const;
  const_reverse_iterator		rbegin() const;
  const_reverse_iterator		rend() const;

  // capacity:
  size_type				size() const;
  size_type				num_elements() const;
  size_type				num_dimensions() const;
 
  // element access:
  template &lt;typename IndexList&gt;
    const element&amp;		operator()(const IndexList&amp; indices) const;
  const_reference		operator[](index i) const;
  const_array_view&lt;Dims&gt;::type	operator[](const indices_tuple&amp; r) const;

  // queries
  const element*		data() const;
  const element*		origin() const;
  const size_type*		shape() const;
  const index*			strides() const;
  const index*			index_bases() const;
  const storage_order_type&amp;     storage_order() const;

  // comparators
  bool operator==(const const_multi_array_ref&amp; rhs);
  bool operator!=(const const_multi_array_ref&amp; rhs);
  bool operator&lt;(const const_multi_array_ref&amp; rhs);
  bool operator&gt;(const const_multi_array_ref&amp; rhs);
  bool operator&gt;=(const const_multi_array_ref&amp; rhs);
  bool operator&lt;=(const const_multi_array_ref&amp; rhs);

  // modifiers:
  template &lt;typename SizeList&gt;
  void			reshape(const SizeList&amp; sizes)
  template &lt;typename BaseList&gt;	void reindex(const BaseList&amp; values);
  void				reindex(index value);
};

</pre>
<p><b>Constructors. </b></p>
<div class="variablelist"><dl class="variablelist">
<dt><span class="term"><pre class="programlisting">template &lt;typename ExtentList&gt;
explicit const_multi_array_ref(TPtr data, 
                     const ExtentList&amp; sizes,
                     const storage_order&amp; store = c_storage_order());
</pre></span></dt>
<dd>
<p>
This constructs a <code class="literal">const_multi_array_ref</code> using the specified
parameters.  <code class="literal">sizes</code> specifies the shape of the
constructed <code class="literal">const_multi_array_ref</code>.  <code class="literal">store</code>
specifies the storage order or layout in memory of the array
dimensions.
</p>
<p><b><code class="literal">ExtentList</code> Requirements. </b>
<code class="literal">ExtentList</code> must model <a href="../../utility/Collection.html" target="_top">Collection</a>.
</p>
<p><b>Preconditions. </b><code class="literal">sizes.size() == NumDims;</code></p>
</dd>
<dt><span class="term">
<pre class="programlisting">explicit const_multi_array_ref(TPtr data,
                     extent_gen::gen_type&lt;NumDims&gt;::type ranges,
                     const storage_order&amp; store = c_storage_order());
</pre></span></dt>
<dd><p><b>Effects. </b>
This constructs a <code class="literal">const_multi_array_ref</code> using the specified
    parameters.  <code class="literal">ranges</code> specifies the shape and
index bases of the constructed const_multi_array_ref. It is the result of 
<code class="literal">NumDims</code> chained calls to 
    <code class="literal">extent_gen::operator[]</code>. <code class="literal">store</code>
specifies the storage order or layout in memory of the array
dimensions. 
</p></dd>
<dt><span class="term"><pre class="programlisting">
const_multi_array_ref(const const_multi_array_ref&amp; x);
</pre></span></dt>
<dd><p><b>Effects. </b>This constructs a shallow copy of <code class="literal">x</code>.
</p></dd>
</dl></div>
</div>
</div>
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